The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen–Cooper–Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose–Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose–Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS–BEC continuum.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems

This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultra-cold Fermi gases This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear many-body theory Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad joint interest to both ultra-cold Fermi gases and nuclear matter, and which will likely help to solve in the future some open problems in nuclear physics (concerning, for instance, neutron stars) Similarities and differences occurring in ultra-cold Fermi gases and nuclear matter will then be emphasized, not only about the relative phenomenologies but also about the theoretical approaches to be used in the two contexts After an introduction to present the key concepts of the BCS-BEC crossover, this report discusses the mean-field treatment of the superfluid phase, both for homogeneous and inhomogeneous systems, as well as for symmetric (spin- or isospin-balanced) and asymmetric (spin- or isospin-imbalanced) matter Pairing fluctuations in the normal phase are then considered, with their manifestations in thermodynamic and dynamic quantities The last two Sections provide a more specialized discussion of the BCS-BEC crossover in ultra-cold Fermi gases and nuclear matter, respectively The separate discussion in the two contexts aims at cross communicating to both communities topics and aspects which, albeit arising in one of the two fields, share a strong common interest

The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems

Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P-F-wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors.

Superfluidity in nuclear systems and neutron stars

This review focuses on applications of the ideas of superfluidity and superconductivity in neutron stars in a broader context, ranging from the microphysics of pairing in nucleonic superfluids to macroscopic manifestations of superfluidity in pulsars. The exposition of the basics of pairing, vorticity and mutual friction can serve as an introduction to the subject. We also review some topics of recent interest, including the various types of pinning of vortices, glitches, and oscillations in neutron stars containing superfluid phases of baryonic matter.

Superfluidity and Superconductivity in Neutron Stars

We obtain the critical magnetic field required for complete destruction of $S$-wave pairing in neutron matter, thereby setting limits on the pairing and superfluidity of neutrons in the crust and outer core of magnetars. We find that for fields $B\ensuremath{\ge}{10}^{17}$ G the neutron fluid is nonsuperfluid---if weaker spin 1 superfluidity does not intervene---a result with profound consequences for the thermal, rotational, and oscillatory behavior of magnetars. Because the dineutron is not bound in vacuum, cold dilute neutron matter cannot exhibit a proper BCS-BEC crossover. Nevertheless, owing to the strongly resonant behavior of the $nn$ interaction at low densities, neutron matter shows a precursor of the BEC state, as manifested in Cooper-pair correlation lengths being comparable to the interparticle distance. We make a systematic quantitative study of this type of BCS-BEC crossover in the presence of neutron fluid spin polarization induced by an ultrastrong magnetic field. We evaluate the Cooper-pair wave function, quasiparticle occupation numbers, and quasiparticle spectra for densities and temperatures spanning the BCS-BEC crossover region. The phase diagram of spin-polarized neutron matter is constructed and explored at different polarizations.

Spin-polarized neutron matter: Critical unpairing and BCS-BEC precursor

The authors examine the phase diagram of neutron-rich nuclear matter, allowing for four competing phases. The resulting phase diagram features two tricritical points as well as crossovers from the BCS phase to a Bose-Einstein deuteron condensate plus a neutron gas. The physics of the individual phases and the transition from weak to strong coupling is traced by examining the Cooper-pair wave function and related quantities.

BCS-BEC crossovers and unconventional phases in dilute nuclear matter

We report on a comprehensive study of the phase structure of cold, dilute nuclear matter featuring a ${}^{3}\phantom{\rule{-0.16em}{0ex}}{S}_{1}$-${}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ condensate at nonzero isospin asymmetry, within wide ranges of temperatures and densities. We find a rich phase diagram comprising three superfluid phases, namely, a Larkin-Ovchinnikov-Fulde-Ferrell phase, the ordinary BCS phase, and a heterogeneous, phase-separated BCS phase, with associated crossovers from the latter two phases to a homogeneous or phase-separated Bose-Einstein condensate of deuterons. The phase diagram contains two tricritical points (one a Lifshitz point), which may degenerate into a single tetracritical point for some degree of isospin asymmetry.

Phase diagram of dilute nuclear matter: Unconventional pairing and the BCS-BEC crossover

The properties of $\isotope[12]{C}$, $\isotope[16]{O}$, and $\isotope[20]{Ne}$ nuclei in strong magnetic fields $B\simeq 10^{17}\,$G are studied in the context of strongly magnetized neutron stars and white dwarfs. The SKY3D code is extended to incorporate the interaction of nucleons with the magnetic field and is utilized to solve the time-independent Hartree-Fock equations with a Skyrme interaction on a Cartesian three-dimensional grid. The numerical solutions demonstrate a number of phenomena, which include a splitting of the energy levels of spin-up and -down nucleons, spontaneous rearrangment of energy levels in $\isotope[16]{O}$ at a critical field, which leads to jump-like increases of magnetization and proton current in this nucleus, and evolution of the intrinsically deformed $\isotope[20]{Ne}$ nucleus towards a more spherical shape under increasing field strength. Many of the numerical features can be understood within a simple analytical model based on the occupation by the nucleons of the lowest states of the harmonic oscillator in a magnetic field.

Carbon-oxygen-neon mass nuclei in superstrong magnetic fields

This contribution will survey recent progress toward an understanding of diverse pairing phenomena in dilute nuclear matter at small and moderate isospin asymmetry, with results of potential relevance to supernova envelopes and proto-neutron stars. Application of ab initio many-body techniques has revealed a rich array of temperature-density phase diagrams, indexed by isospin asymmetry, which feature both conventional and unconventional superfluid phases. At low density there exist a homogeneous translationally invariant BCS phase, a homogeneous LOFF phase violating translational invariance, and an inhomogeneous translationally invariant phase-separated BCS phase. The transition from the BCS to the BEC phases is characterized in terms of the evolution, from weak to strong coupling, of the pairing gap, condensate wave function, and quasiparticle occupation numbers and spectra. Additionally, a schematic formal analysis of pairing in neutron matter at low to moderate densities is presented that establishes conditions for the emergence of both conventional and unconventional pairing solutions and encompasses the possibility of dineutron formation.

http://iopscience.iop.org/article/10.1088/1742-6596/702/1/012012/pdf

Martin Stein

Papers

Spin-polarized neutron matter: Critical unpairing and BCS-BEC precursor

BCS-BEC crossovers and unconventional phases in dilute nuclear matter

Phase diagram of dilute nuclear matter: Unconventional pairing and the BCS-BEC crossover

Carbon-oxygen-neon mass nuclei in superstrong magnetic fields

Conventional and Unconventional Pairing and Condensates in Dilute Nuclear Matter